3,619 research outputs found

### Lorentz Invariant Baryon CHPT

Using the example of the elastic $\pi N$-amplitude, we discuss the low energy
expansion of QCD amplitudes in the sector with baryon number one. We show that
the chiral expansion of these amplitudes breaks down in certain regions of
phase space and present a framework which leads to a coherent description
throughout the low energy region, while keeping Lorentz and chiral invariance
manifest at every stage of the calculation. We explain how to construct a
representation of the pion nucleon scattering amplitude in terms of functions
of a single variable, which is valid to $O(q^4)$ and properly accounts for the
$\pi\pi$- and $\pi N$-cuts required by unitarity.Comment: Latex, 12 pages. Plenary talk given at "Chiral Dynamics 2000: Theory
and Experiment", Newport News, USA, 17-22 July 200

### Low energy analysis of pi N --> pi N

We derive a representation for the pion nucleon scattering amplitude that is
valid to the fourth order of the chiral expansion. To obtain the correct
analytic structure of the singularities in the low energy region, we have
performed the calculation in a relativistic framework (infrared
regularization). The result can be written in terms of functions of a single
variable. We study the corresponding dispersion relations and discuss the
problems encountered in the straightforward nonrelativistic expansion of the
infrared singularities. As an application, we evaluate the corrections to the
Goldberger-Treiman relation and to the low energy theorem that relates the
value of the amplitude at the Cheng-Dashen point to the \sigma-term. While
chiral symmetry does govern the behaviour of the amplitude in the vicinity of
this point, the representation for the scattering amplitude is not accurate
enough to use it for an extrapolation of the experimental data to the
subthreshold region. We propose to perform this extrapolation on the basis of a
set of integral equations that interrelate the lowest partial waves and are
analogous to the Roy equations for \pi\pi scattering.Comment: 97 pages (LaTeX), 16 figures. Two references added, correction in
table one. Published versio

### Enhanced non-perturbative effects through the collinear anomaly

We show that non-perturbative effects are logarithmically enhanced for
transverse-momentum-dependent observables such as q_T-spectra of electroweak
bosons in hadronic collisions and jet broadening at e^+e^- colliders. This
enhancement arises from the collinear anomaly, a mechanism characteristic for
transverse observables, which induces logarithmic dependence on the hard scale
in the product of the soft and collinear matrix elements. Our analysis is based
on an operator product expansion and provides, for the first time, a
systematic, model-independent way to study non-perturbative effects for this
class of observables. For the case of jet broadening, we relate the leading
correction to the non-perturbative shift of the thrust distribution.Comment: 5 pages, 2 figures. v2: Minor changes, references added. Journal
versio

### Mathematic & mathematics education: searching for common ground, edited by M. Fried and T. Dreyfus, New York, Springer, 2014, 402 pp., ÂŁ90, ISBN 978-94-007-7472-8

This is an Accepted Manuscript of an article published by Taylor & Francis in Research in Mathematics Education on 22nd Aug 2014, available online: http://dx.doi.org/10.1080/14794802.2014.93735

### Isospin violation in the vector form factors of the nucleon

A quantitative understanding of isospin violation is an increasingly
important ingredient for the extraction of the nucleon's strange vector form
factors from experimental data. We calculate the isospin violating electric and
magnetic form factors in chiral perturbation theory to leading and
next-to-leading order respectively, and we extract the low-energy constants
from resonance saturation. Uncertainties are dominated largely by limitations
in the current knowledge of some vector meson couplings. The resulting bounds
on isospin violation are sufficiently precise to be of value to on-going
experimental studies of the strange form factors.Comment: 13 pages, 8 figures, uses RevTe

### On the Structure of Infrared Singularities of Gauge-Theory Amplitudes

A closed formula is obtained for the infrared singularities of dimensionally
regularized, massless gauge-theory scattering amplitudes with an arbitrary
number of legs and loops. It follows from an all-order conjecture for the
anomalous-dimension matrix of n-jet operators in soft-collinear effective
theory. We show that the form of this anomalous dimension is severely
constrained by soft-collinear factorization, non-abelian exponentiation, and
the behavior of amplitudes in collinear limits. Using a diagrammatic analysis,
we demonstrate that these constraints imply that to three-loop order the
anomalous dimension involves only two-parton correlations, with the possible
exception of a single color structure multiplying a function of conformal cross
ratios depending on the momenta of four external partons, which would have to
vanish in all two-particle collinear limits. We argue that such a function does
not appear at three-loop order, and that the same is true in higher orders. Our
formula predicts Casimir scaling of the cusp anomalous dimension to all orders
in perturbation theory, and we explicitly check that the constraints exclude
the appearance of higher Casimir invariants at four loops. Using known results
for the quark and gluon form factors, we derive the three-loop coefficients of
the 1/epsilon^n pole terms (with n=1,...,6) for an arbitrary n-parton
scattering amplitude in massless QCD. This generalizes Catani's two-loop
formula proposed in 1998.Comment: 46 pages, 9 figures; v2: improved treatment of collinear limits,
references added; v3: improved discussion of non-abelian exponentiation,
references updated; v4: typo in eq. (17) fixed, references updated; v5:
additional term in (17

### Sudakov Resummation for Subleading SCET Currents and Heavy-to-Light Form Factors

The hard-scattering contributions to heavy-to-light form factors at large
recoil are studied systematically in soft-collinear effective theory (SCET).
Large logarithms arising from multiple energy scales are resummed by matching
QCD onto SCET in two stages via an intermediate effective theory. Anomalous
dimensions in the intermediate theory are computed, and their form is shown to
be constrained by conformal symmetry. Renormalization-group evolution equations
are solved to give a complete leading-order analysis of the hard-scattering
contributions, in which all single and double logarithms are resummed. In two
cases, spin-symmetry relations for the soft-overlap contributions to form
factors are shown not to be broken at any order in perturbation theory by
hard-scattering corrections. One-loop matching calculations in the two
effective theories are performed in sample cases, for which the relative
importance of renormalization-group evolution and matching corrections is
investigated. The asymptotic behavior of Sudakov logarithms appearing in the
coefficient functions of the soft-overlap and hard-scattering contributions to
form factors is analyzed.Comment: 50 pages, 10 figures; minor corrections, version to appear in JHE

### Information on the structure of the a1 from tau decay

The decay $\tau\to \pi\pi\pi\nu$ is analysed using different methods to
account for the resonance structure, which is usually ascribed to the a1. One
scenario is based on the recently developed techniques to generate axial-vector
resonances dynamically, whereas in a second calculation the a1 is introduced as
an explicit resonance. We investigate the influence of different assumptions on
the result. In the molecule scenario the spectral function is described
surprisingly well by adjusting only one free parameter. This result can be
systematically improved by adding higher order corrections to the iterated
Weinberg-Tomozawa interaction. Treating the a1 as an explicit resonance on the
other hand leads to peculiar properties

### Direct photon production with effective field theory

The production of hard photons in hadronic collisions is studied using
Soft-Collinear Effective Theory (SCET). This is the first application of SCET
to a physical, observable cross section involving energetic partons in more
than two directions. A factorization formula is derived which involves a
non-trivial interplay of the angular dependence in the hard and soft functions,
both quark and gluon jet functions, and multiple partonic channels. The
relevant hard, jet and soft functions are computed to one loop and their
anomalous dimensions are determined to three loops. The final resummed
inclusive direct photon distribution is valid to next-to-next-to-leading
logarithmic order (NNLL), one order beyond previous work. The result is
improved by including non-logarithmic terms and photon isolation cuts through
matching, and compared to Tevatron data and to fixed order results at the
Tevatron and the LHC. The resummed cross section has a significantly smaller
theoretical uncertainty than the next-to-leading fixed-order result,
particularly at high transverse momentum.Comment: 42 pages, 9 figures; v2: references added, minor changes; v3: typos;
v4: typos, corrections in (16), (47), (72

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